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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:14
IMO A.
Statement 1: 3X + 30 leaves remainder 93 when divided by 120. The numbers in this form would be 93,213,333,453... X values for these would respectively would be  30,70,110,150... When these values are divided by 40, it always leaves a remainder as 30. Hence, this statement is sufficient.
Statement 2: 5X  10 leaves remainder 15 when divided by 20. The numbers in this form would be 15,35,55,75... X values for these would respectively would be  5,9,13,17... When these values are divided by 40, does not give a fixed value. Hence, this statement is not sufficient.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:16
The question states that what is the remainder when X is divided by 40 Statement 1: 3X + 30 leaves remainder of 93 when divided by 120 Let X = 21, therefore, 3(21) + 30 = 93 Thus, 93/120 gives remainder of 93 therefore, 93/40 gives remainder of 13 Let X = 61, therefore, 3(61) + 30 = 213 thus, 213/120 gives remainder of 93 therefore, 213/40 gives remainder of 13 similarly, let X = 101, therefore, 3(101) + 30 = 333 thus, 333/120 gives remainder of 93 therefore, 333/40 gives remainder of 13 Therefore this statement is sufficient (AD) Statement 2: (5X  10)/20 gives remainder of 15 let X = 5, therefore (5x5  10)/20 = 15/20 gives remainder of 15 therefore, 5/40 gives remainder of 5 let X = 9, therefore (5x9  10)/20 = 35/20 gives remainder of 15 therefore, 9/40 gives remainder of 9 Not sufficient Hence answer choice A.
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:19
from statement (1),\(3x + 30 = 120a + 93\) \(x = 40a + 21\) , so the possible values of \(x\) are (\(21,61,101,...\)), which all gives \(21\) as a reminder upon dividing by \(40\) > sufficientfrom statement (2),\(5x  10 = 20b + 15\) \(x = 4b + 5\), so the possible values of x are (\(5,9,13,...\)) which gives different values (\(5,9,13,...\)) upon dividing by \(40\) > insufficientA
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:27
IMO A
Have to find: Remainder of \(X/40\)
Statement 1 > \(\frac{(3X + 30)}{120}\) gives a remainder of 93. Substitute for X based on this statement. For X = 21, \(\frac{(3X + 30)}{120}\) gives the remainder of 93 and \(X/40\) gives a remainder of 21. For X = 101, \(\frac{(3X + 30)}{120}\) gives the remainder of 93 and \(X/40\) gives a remainder of 21 again. > Sufficient
Statement 2 > \(\frac{(5X  10)}{20}\) gives a remainder of 15. Substitute for X based on this statement. For X = 5, \(\frac{(5X  10)}{20}\) gives the remainder 15 and \(X/40\) gives the remainder 5. For X = 9, \(\frac{(5X  10)}{20}\) gives the remainder 15, but \(X/40\) gives the remainder 9. > Insufficient



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:32
3x +30 will always yield x as 39,79,119 and Soo on
So.remainder will be always 39
But 5x10 will have values of x different as 13,17 so we have different remainder values
A it is
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:34
(1) 3X + 30 leaves remainder 93 when divided by 120.
We can express this fraction as
\(\frac{3(x+10)}{120} = n + \frac{93}{120}\) where n is the quotient
This reduces to
\(\frac{(x+10)}{40} = n + \frac{31}{40}\)
So when \(x+10\) is divided by \(40\), the remainder is \(31\)
When \(10\) is divided by \(40\), the remainder is \(10\) so when \(x\) is divided by \(40\), the remainder must be \(21\)
1 is sufficient
(2) 5X  10 leaves remainder 15 when divided by 20.
Lets express this fraction as \(\frac{5(x2)}{20} = \frac{m+15}{20}\)
This reduces to \(\frac{(x2)}{4} = m+\frac{3}{4}\)
x2 leaves a remainder of 3 when divided by 4
Not sufficient to find out the remainder when x is divided by 40
2 is insufficient
Answer is (A)



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:37
What is the remainder when positive integer X is divided by 40?
STATEMENT (1) 3X + 30 leaves remainder 93 when divided by 120 from this statement, 3X+30 can be written as 3X+30 = 120K + 93(K=0,1,2,3,4........) 3(X+10) = 3(40K+31) X+10 = 40K+31 X=40K+21
X can be 21,61,101,141......... X divided by 40 gives the remainder 21 so SUFFICIENT
STATEMENT (2) 5X  10 leaves remainder 15 when divided by 20. from this statement, 5X10 can be written as 5X10 = 20K+15(K=0,1,2,3,4......) 5(X2) = 5(4K+3) X2 = 4K+3 X = 4K+5
X can be 5,9,13............45,49,53..... X divided by 40 gives remainder 5,9,13,... so INSUFFICIENT
A is the answer



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:51
We can express x=40q+r Where q is a quotient and r is the remainder (both nonnegative integers) Always note that remainder cant be more than the divisor (in our case 40)
1 stm > We can insert above value of x to get: 3(40q+r)+30=120q+3r+30 We can observe that 120q is divisible by 120, so 3r+30 divided by 120 will leave 93 as a remainder We can manipulate with some noble numbers to get 93 remainder when divided by 120 and those lowest integers are 93 and 213 1) 3x+30=93 r=21 Valid as r<40 2) 3r+ 30=213 r=61 Not Valid r>40 and all other integers will give the value of r more than 40. Only one option is valid r=21
Sufficient
2 stm > The same process as above 5(40q+r)10=200q+5r10 (200q is divisible by 20) 5r10 divided by 20 leaves remainder 15 1) 5r10=15 r=5 (r<40) 2) 5r10=35 r=9 (r<40)
at least two values are possible
Not sufficient
IMO ANS: A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 10:01
We are required to find remainder when \(x\) an unknown positive integer is divided by 40, i.e. the value of "r" where \(x=40m+r\):
(1) 3X + 30 leaves remainder 93 when divided by 120.  This means that \(3x+30=120n+93\) ==>> (divide equation by 3) \(x+10=40n+31\) ==>> \(x=40n+21\). So the remainder of \(\frac{x}{40}\) is 21. Sufficient.
(2) 5X  10 leaves remainder 15 when divided by 20.  This implies that \(5x10=20k+15\) ==>> (divide equation by 5) \(x2=4k+3\)==>>\(x=4k+5\) ==> \(x=4p+1\), meaning that when x is divided by 4, the quotient is an integer p and the remainder is 1. However, we are unable to derive the remainder when \(x\) is divided by 40, insufficient.
Correct answer is A.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 10:09
IMO A
What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120.
Say q is quotient, then from st.1 => 3X + 30 = 120q + 93 => 3X = 120q + 63 => X = 40q + 21 Clearly, remainder is 21 when X is divided by 40 Sufficient
(2) 5X  10 leaves remainder 15 when divided by 20.
Say q is quotient, then from st.2 => 5X  10 = 20q + 15 => 5X = 20q + 25 => X = 4q + 5 Now from this equation we can get X = 5, 9, 13, 17, 21, etc. And if 5 is divided by 40, the remainder is 5, but if 9 is divided by 40, the remainder is 9 So, we have different values. Insufficient



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 10:12
(1) 3X + 30 leaves remainder 93 when divided by 120. X will be 21, 61 and so on, remainder will always be 21. Sufficient
(2) 5X  10 leaves remainder 15 when divided by 20. Different remainders for the values of X. Not Sufficient.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 10:20
(1) 3X + 30 leaves remainder 93 when divided by 120. That means 3x+3093 is divisible by 120 3x63 = 120a (where 'a' is a positive integer) 3(x21)=120a x21 = 40a so we can determine the remainder as 21 when divided by 40. Sufficient
(2) 5X  10 leaves remainder 15 when divided by 20. 5x25 is divisible by 20 5(x5)=20a x5=4a We will not be able to calculate remainder when x is divisible by 40 from this equation. Insufficient.
IMO A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 10:20
Quote: What is the remainder when positive integer X is divided by 40? X is integer and x > 0 We need to identify if it is possible to find a remainder when X is divided by 40 in this Data Sufficiency (DS) question: Let us analyze the statements: Statement 1:(1) 3X + 30 leaves remainder 93 when divided by 120. Let us write it down as a formula: \(3X + 30 = 120*a + 93\), where a is the number of times 120 is repeated in 3X + 30 \(3X = 120*a + 93  30 = 120*a + 63 = 3 * (40*a + 21)\) \(X = 40*a + 21\) Thus, 21 is remainder when X is divided by 40. Sufficient. Statement 2: (2) 5X  10 leaves remainder 15 when divided by 20. Again, let us represent it with the formula: \(5X  10 = 20*b + 15\), where b is the number of times 20 is repeated in 5X  10 \(5X = 20*b + 15 + 10 = 20*b + 25 = 5 * (4*b + 5)\) \(X = 4*b + 5\) Unfortunately, we do not possess information whether b is equal to 1, 10 or 15, and for this reason are unable to answer the question about the remainder using this statement alone. Insufficient. Answer: A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 10:39
What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120. > correct: 3X+30 = 120*d + 93 => X+10 = 40*d + 31 => X = 40 *d + 21, so if X is divided by 40, the reminder will be 21 (2) 5X  10 leaves remainder 15 when divided by 20. > 5X 10 = 20 * D + 15 => X 2 = 4 * D + 3 => X = 4 * D + 5 => X = 4* (D+1) + 1, now case1: if X =61, then if 61 divided by 4, reminder will be 1 & if 61 divided by 40, reminder will be 21 but case2: if X =41, then if 41 divided by 4, reminder will be 1 & if 41 divided by 40, reminder will be 1. So different reminder for different cases.
SO the Answer is A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 10:44
To find,
Remainder of X when X is divided by 40.
We know,
Dividend = Divisor * Quotient + Remainder
Let us check the two options 
Option 1: 3X + 30 leaves remainder 93 when divided by 120.
=> 3*X + 30 = 120 * Quotient + 93 => X + 10 = 40 * Quotient + 31 => X = 40 * Quotient + 21
Hence, X whenever divided by 40 will give a remainder of 21.
Hence option 1 is sufficient.
Option 2: 5X  10 leaves remainder 15 when divided by 20.
=> 5*X  10 = 20 * Quotient + 15 => X  2 = 4 * Quotient + 3 => X = 4 * Quotient + 5 => X = 4 * Quotient + 4 + 1 => X = 4 * (Quotient + 1) + 1
Hence, X whenever divided by 4 will give a remainder of 1.
Now, if X is 5 (satisfying above condition in option 2) then it will give a remainder of 5 when divided by 40. Now, if X is 9 (satisfying above condition in option 2) then it will give a remainder of 9 when divided by 40. Now, if X is 45 (satisfying above condition in option 2) then it will give a remainder of 5 when divided by 40. Now, if X is 53 (satisfying above condition in option 2) then it will give a remainder of 13 when divided by 40.
Hence, option 2 is insufficient.
Answer: A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 11:02
IMOA
Remainder when positive integer X is divided by 40
(1) 3X + 30 leaves remainder 93 when divided by 120.
3X+30= 120K + 93 => X+10= 40K + 31 [K = integer] => X21 = 40K => X21= { 0, 40, 80, ........40K} => X= 21, 61, 81,....40K+21 Remainder (X/40)= 21
Sufficient
(2) 5X  10 leaves remainder 15 when divided by 20. =>.5X10=20K+15 => 5X= 20K+25 => X= 4K+5 => X= {5,9,13,17...........4K+5} Remainder (X/40)= {5,9,13,17.....}
Not Sufficient



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 11:55
What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120. (2) 5X  10 leaves remainder 15 when divided by 20.
Stmt 1: if x =61, then 3*61+30 = 213 , which results in 93 when divided by 120 if x =141, then 3*141+30 = 453 , which results in 93 when divided by 120. Different values of X give similar remainder. so sufficient.
Stmt 2: if x =9, then 5*910 = 35 , which results in 15 when divided by 20 if x =13, then 5*1310 = 55 , which results in 15 when divided by 20, Different values of X give different remainder. so insufficient. So, the correct answer choice is (A)



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 12:19
What is the remainder when positive integer X is divided by 40?
40q+r = X ..... q is quotient and r is remainder. We have to find r.
(1) 3X + 30 leaves remainder 93 when divided by 120.
120q+93 = 3X + 30 120q+63 = 3X 40q+21 = X ... This is in the same form as 40q+r=X
Therefore r = 21
(1) IS SUFFICIENT
(2) 5X  10 leaves remainder 15 when divided by 20.
20q+15 = 5X10
20q + 25 = 5X
4q + 5 = X
It is not possible to represent X in the form of 40q+r....
X could be 9 with remainder 9, or x could be 45 with remainder 5.
(2) IS NOT SUFFICIENT
ANSWER: A  1 Alone is SUFFICIENT



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What is the remainder when X is divided by 40?
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Updated on: 18 Jul 2019, 04:43
What is the remainder when positive integer X is divided by 40? (1) 3X + 30 leaves remainder 93 when divided by 120. (2) 5X  10 leaves remainder 15 when divided by 20. condition 1,
3x + 30 leaves remainder 93, when divided by 120assume first no 93, so 3x is 63 hence x is 21. so remainder is 21 if divided by 40 next x will be increased by 120/ coefficient of x ie 120/3 is 40. because other no is just an addition which will always maintain the same distance so next x is 61 which gives , 183 + 30 is 213, if divided by 120 will leave remainder 93 and so on.. so x can be 21,61,101.... so on . so whatever the remainder is 21 when divided by 40 so this is sufficient, ans is always 21. condition 2,
5x10 , remainder 15. when divided by 20assume n = 15, which gives, 5x = 25 so x =5. , so remainder if divided by 40 is 5 next x will be increased by 20/ coefficient of x ie 20/5 which is 4. so next x is 5 + 4 is 9, which gives, 4510, 35 if divided by 20 will leave 15 and so on x can be 5,9,13,17 .... so on and each leaves different remainder when divided by 40 so clearly insufficient so ans is A
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Originally posted by ccheryn on 17 Jul 2019, 12:50.
Last edited by ccheryn on 18 Jul 2019, 04:43, edited 3 times in total.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 12:51
What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120. Statement 1 can be written as 3X+30 = 120k+93 Dividing by 3 we get X+10=12k+31 > X=40k+21. Dividing by 40 we get X/40 = k+21/40. Remainder is 21. Hence Statement 1 is sufficient.
(2) 5X  10 leaves remainder 15 when divided by 20. Statement 2 can be written as 5X10=20k+15 > 5X=20k+25 Dividing by 5 we get X=4k+5 Dividing by 40 we get X/40 = (4k+5)/40 If k = 0, we get remainder as 5. If k = 1, we get remainder as 9. Therefore we don't get fixed remainder in this case. Hence statement 2 is not sufficient.
Statement 1 alone is sufficient.
Answer Choice: A




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